'I'm running bad,' is a phrase you will often hear poker players use to describe periods of bad luck or variance. In poker, it sometimes just feels as if the cards are conspiring against you. Another 40 games are given Variance Tournoi Poker upon deposit on the second day after the first deposit Variance Tournoi Poker (min £20), and an additional 40 games are given Variance Tournoi Poker upon deposit on the third day (min £20). Winnings won with games that require deposit, have to be wagered 35x.

Professional poker players often describe their vocation as “a hard way to make an easy living”. One of the most difficult aspects of the game that a professional poker player must deal with is the inconsistency in income. Despite employing a strong skill set and the benefits of years of experience, many poker players still come home with less money in their pocket than when they arrived at the tables. These ups and downs of poker are often collectively known as “variance”.

What is Variance?

How Variance and Statistical Chance Works In Poker They go together in poker because as all of us recognize in poker that sometimes you win and then sometimes you lose. You may realize when you are confronted with variance there are statistical chances of these fingers swing forcefully headed for or contrary to you. High Variance Poker vs. Low Variance Poker April 18, 2009 October 5, 2005 by Bill Rini I was commenting on something over on the Full Tilt message boards the other day and I started me thinking about the concept of variance.

In statistical terms, variance is used to examine the differences between an individual result and the average for a set of results. These results can be represented as data points in a set to determine the fluctuations within that set.

We’ll demonstrate how to calculate variance with a small sample data set. If you were to track the results for your previous sessions at a $3/$6 fixed-limit hold’em cash game, they could read:

-11, +85, -30, +144, +9, +30, -87

Each of these results represents a data point in a set of seven numbers.

The total of these seven sessions equals +140 (-11 + 85 – 30 + 144 + 9 + 30 – 87 = 140)

The average of these seven sessions equals +20 (140/7).

The variance is the sum of the squares of the differences between each data point and the mean.

For the first result, (20 – (-11)) = (20 + 11) = 31. 31^2 = 961

Follow the same procedure for each result and you get these corresponding numbers:

961, 4225, 2500, 15376, 121, 100, 11449

Add up these numbers and divide by seven to get the variance:

961 + 4225 + 2500 + 15376 + 121 + 100 + 11449 = 34732

34732/7 = 4961.71

The standard deviation, another measure of volatility, is the square root of the variance:

SQRT(4961.71) = 70.43

The most frequent results lie within one standard deviation (+/- 70) of the mean (+20). With these results, a player should expect to finish a session somewhere between -50 (20-70) and +90 (20+70).

However, many of these data points lie outside that range. Are these results the products of bad luck, bad cards or bad play?

Variance and Sample Sizes

The more data points a sample size contains, the more accurate and reliable the measurements of variance and standard deviation will be. The seven-point data set included here is obviously much too small to give an accurate estimate of how a player performs at a 3/6 limit hold’em game. Also, more data points will give the player more information on how to manage the inevitable ups and downs involved in cash games.

Variance and the Central Limit Theorem

Another important mathematical concept that comes with sample size is the “Central Limit Theorem”. This concept states that, as the number of data points in a set grows, a plot of those points on a graph will resemble a normal statistical distribution, as seen in the classic “Bell Curve”.

The guiding principle is that, the larger the sample size, the more data points that will fall at or near the average. This measure of variance gives the player a more accurate idea as to what to expect from his results.

Variance and Luck

Even in the most distinguished poker careers, a player will have sessions where he has wins (or losses) that go two or more standard deviations away from the average. Many inexperienced players attribute these results to luck, but they are within the realm of possibility shown in the Bell Curve. These data points are known as “outliers” and, individually, have little effect on the variance seen over a career. If these “outlying” results continue to appear, however, they may signal the start of a new trend.

Variance and Bankrolls

A sufficient poker bankroll is necessary to act as a cushion against variance. Some players may believe that, with just a few positive results at a $1/$2 no-limit hold’em game, they are ready to jump into a $2/$5 or $5/$10 game, regardless of their bankroll size. When the variance swings in the negative direction, as it inevitably will, a depleted bankroll could send the player to either a lower-stakes game or out of the game entirely.

Variance and Structure

Some poker games, as well as some betting structures, are prone to have higher variance than others. For instance, a $3/$6 fixed-limit hold’em game will have much less variance than a $1/$2 no-limit hold’em game due almost exclusively to the betting structure. In the $3/$6 limit game, the maximum bet a player can make on the river is $24 (bet-raise-re-raise-cap). In the no-limit game, a player can bet his entire stack at any time, which may be hundreds of dollars. These bet sizes can cause huge swings in variance.

Variance in Poker Tournaments

Despite the allure of fame and glory presented by televised events, no-limit hold’em tournaments are shining examples of the deceptive power of variance. Most professional players (including many famous faces on the tournament circuit) make more of their living through cash games and only enter the most prestigious (and lucrative) tournaments due to the high variance involved. Most major tournament winners are “outliers”, as up to ninety percent of all tournament players walk home empty-handed.

Variance and Playing Styles

In a previous piece, we examined the four primary playing styles (loose-passive, loose-aggressive, tight-passive and tight-aggressive). Just as the tight-aggressive style has been shown to be the most profitable, it also often results in the lowest variance. Both the loose-passive and the tight-passive players depend on catching cards to win hands (a high-variance strategy) while the loose-aggressive style relies on big bets to push players off hands. The tight-aggressive method relies on strong starting hand selection, infrequent bluffs and a well-founded understanding of probabilities, all of which contribute to reducing variance.

Variance and Emotion

The effects of big wins and staggering losses are not strictly limited to a player’s bankroll. The emotional roller coaster that comes with big swings in variance can also affect how a player approaches the game. Players who have become accustomed to big wins may lose their cool when confronted with a crushing loss. One bad session can set a player “on tilt” and wreck both his skills and his confidence.

How to Deal with Variance

Variance Tournoi Poker Game

Shifts in variance can be as unpredictable and dangerous as shifts in the weather: everybody complains about them, but no one can do anything to prevent it. The most important aspect of success in poker lies in treating each session or tournament as a continuation in one long game. Experienced players understand that their success or failure as a player does not lie in the results of a single tournament or a handful of cash-game sessions. Each session represents only a single data point: a consistent approach will often reduce (but never entirely eliminate) variance.

Conclusion

Former World Series of Poker Main Event Champion Chris “Jesus” Ferguson once said that poker is “100 percent luck and 100 percent skill”. The turn of each card is the result of luck, but how a player responds to that unpredictable event is the product of skill, practice and experience. The ability to manage the game’s inherent variance is a skill on par with calculating odds and outs in terms of how successful a player can eventually become.

By Gerald Hanks

Gerald Hanks is from Houston Texas, and has been playing poker since 2002. He has played cash games and no-limit hold’em tournaments at live venues all over the United States.

Variance:The Bane of Every Poker Player's Life

The fact or quality of being different, divergent, or inconsistent”

As soon as I first picked up the game back in 2005 it was obvious just how painful my relationship with luck was going to be if I ever wanted to play this game for a living. Looking back from today I really had no idea just how bad things could possibly get. Come to think of it, neither did the entire poker community!

My first poker experience came through online MTTs, and the standard advice back in the day was for professionals to have at least one hundred tournament buy ins in their bankroll. Little did we know that this was to prove way too cavalier. Especially as the games became tougher and tougher.

These days people are now more likely to suggest at least three hundred buy ins for tournaments, and at least fifty buy ins for NL cash games, with PLO needing even more. This is not conservative either, it's supposed to be a basic minimum.

I can say for certain now, as an eleven year veteran of the game that variance is still not understood by the vast majority of casual players. The main problem being that they are not able to play the volume required to ride through the swings in reasonable time, with a downswing lasting months,maybe years rather than weeks for cash game players. Recreational live tournament players will possibly not even manage to play enough over the rest of their lives to get any kind of an accurate understanding of just how good they are.

So how can we better understand the variance we can expect to experience?

What Does a Variance Calculator Do Exactly?

The calculator is a tool which can simulate millions of hands or tournaments, and scientifically show us the results from a best case scenario to the worst case.

It is never going to prove anything with one hundred percent certainty, but it will show us close enough to suit our purposes giving us an idea of just how much luck is involved, and what kind of time scale is involved to play through an average downswing.

By inputting various statistics from our database we will also be able to see over a particular sample size what percentage of the time we can expect to be in profit. Along with advice on required bankroll size to stay within a reasonable risk of ruin percentage.

In today's tougher games, much is being said about how the mental game side of poker is becoming more important to maximize your results.

The Cash Game Variance Calculator

The best application out there today looks to be here.

Let's take a look at how the cash game calculator works.

Here I want to use as an example a recreational player who works full time so only finds time for 25000 hands per month. This player has a decent win rate of 2.5BB/100. Not to be confused with BB/100 which is twice the BB/100 that you need to enter.

Here we can see some samples showing that even being a decent player, over a small sample size of 25000 hands there's still a fairly high chance of losing money.

There is also a report showing some useful metrics.

As we can see from all this data, 25000 hands for many casual players can take quite a long time to play, and even if they know they are decent enough to win well in the games they play in, there is still a high chance of being down money.

The Tournament Variance Calculator

The best application out there today looks to be here.

Even new players to the game who read about poker, and study the game to any extent will likely have heard about the extreme variance experienced by MTT players.

In this example our hero is a recreational player who finds time for 1500 tournaments in a year.

HisROI % is a healthy 35%, but nothing spectacular. He plays only $5 buy in events with an average of five thousand entrants. Each tournament pays out prizes to the top fifteen percent of finishers.

Here we can see that there is roughly a twenty five percent chance that he will be down money at the year's end. Fifty percent of the time he can expect to have won more than $2285, with the worst case being a total loss of more than $3400.

Can you imagine what an unprepared casual player would be thinking if they had lost $3400? This is why we need to do this work away from the table.

Here is a random selection of twenty samples. As you can see there is still the possibility of going on a huge heater and making a nice profit. But there's no guarantees!

Similar to the cash game calculator we also get a detailed chart of statistical data.

Conclusion

In both examples we saw a competent player stand a fairly high chance of losing money over a single month,and over a full year.

Once you have experimented with different permutations you may even wish to change your game of choice. One point which stands out more than any other is how live poker players need the patience of a saint. They simply cannot look at poker in terms of months. Even for the professionals only hardcore cash game grinders can expect to feel a degree of certainty after a year's play. Live MTT players can expect a long wait, there just aren't enough days in the week.

For online players the long run can come around much sooner, but for those of you with jobs and family commitments it can still be a frustratingly long time before you see the fruits of your labor.

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